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If the curve L is x ^ 2 + y ^ 2 = 9, then the curve integral ∫ (x ^ 2 + y ^ 2) ds =? I figured it out to be 54 π. Why don't I have that answer
∫(x^2+y^2)ds
=∫ 9 ds
=9*2π*3
=54π
Curvilinear integration can simplify the function to be integrated by curvilinear equation;
The integrand function is 1, and the integral result is the arc length of the curve, that is, the circumference of the circle
If you don't have this answer, you are wrong
Let l be the line segment connecting o (0,0) and a (1,1), then the curve integral ∫ L (x + y) ds=
The segment connecting (0,0) and (1,1) is y = x, dy / DX = 1
∫L (x + y) ds
= ∫(0→1) (x + x)√(1 + (dy/dx)²) dx
= ∫(0→1) 2x√(1 + 1) dx
= √2 * x²|(0→1)
= √2
It is known that the absolute value of X is 1 / 2 of the absolute value of 6 y and XY is less than 0, so the value of y of X can be obtained
If XY is less than 0, one of them is positive and the other is negative
So y / X is negative
So y / x = - (1 / 2) / 6 = - 1 / 12
If x is less than y and less than 0, then what is the result of the absolute value of X out of X, XY out of XY?
x＜y＜0,|x|/x=?|xy|/(xy)=?
one
x＜0,|x|=-x
|x|/x=-x/x=-1;
two
x＜0,y＜0
xy＞0
|xy|=xy
|xy|/(xy)=xy/(xy)=1
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